In this article, an engineering/physical dynamic system including losses is analyzed inrelation to the stability from an engineer’s/physicist’s point of view. Firstly, conditions for a Hamiltonian to be an energy function, time independent or not, is explained herein. To analyze stability of engineering system, Lyapunov-like energy function, called residual energy function is used. The residual function may contain, apart from external energies, negative losses as well. This function includes the sum of potential and kinetic energies, which are special forms and ready-made (weak) Lyapunov functions, and loss of energies (positive and/or negative) of a system described in different forms using tensorial variables. As the Lypunov function, residual energy function is defined as Hamiltonian energy function plus loss of energies and then associated weak and strong stability are proved through the first time-derivative of residual energy function. It is demonstrated how the stability analysis can be performed using the residual energy functions in different formulations and in generalized motion space when available. This novel approach is applied to RLC circuit, AC equivalent circuit of Gunn diode oscillator for autonomous, and a coupled (electromechanical) example for nonautonomous case. In the nonautonomous case, the stability criteria can not be proven for one type of formulation, however, it can be proven in the other type formulation.

A wireless sensor system is an essential aspect in many fields. It consists of a great deal of sensor nodes. These sensor networks carry out a number of tasks, including interaction, distribution, recognition, and power supply. Data is transmitted from source to destination and plays an important role. Congestion may occur during data transmission from one node to another and also at cluster head locations. Congestion will arise as a result of either traffic division or resource allocation. Energy will be wasted due to traffic division congestion, which causes packet loss and retransmission of removed packets. As a result, it must be simplified; hence there are a few Wireless sensor networks with various protocols that will handle Congestion Control. The Deterministic Energy Efficient Clustering (DEC) protocol, which is fully based on residual energy and the token bucket method, is being investigated as a way to increase the energy efficiency. In the event of congestion, our proposal provides a way to cope with it and solves it using this method to improve lifespan of the sensor networks. Experiments in simulation show that the proposed strategy can significantly enhance lifetime, energy, throughput, and packet loss.